$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 5x - 6$ and $ JT = 7x - 16$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {5x - 6} = {7x - 16}$ Solve for $x$ $ -2x = -10$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 5({5}) - 6$ $ JT = 7({5}) - 16$ $ CJ = 25 - 6$ $ JT = 35 - 16$ $ CJ = 19$ $ JT = 19$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {19} + {19}$ $ CT = 38$